Suppose the students construct a 95% confidence interval for the true weight of their rocks. Whose interval do you expect to be more precise (narrower)? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both intervals would be equally precise.

(i) The student who weighed the rock 20 times.

Step-by-step explanation:

The margin of error of a confidence interval is:

In which z is related to the confidence level, is the standard deviation of the population and n is the size of the sample.

From the equation above, the larger the size of the sample, the lower the margin is, that is, the narrower the interval is.

In this question:

A student weighed the rock 20 times and other the 5. From above, the one who weighed the rock 20 times will have the more precise interval.

So the correct answer is:

(i) The student who weighed the rock 20 times.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .